An overview on nonlinear porous flow in low permeability porous media

This paper gives an overview on nonlinear porous flow in low permeability porous media, reveals the microscopic mechanisms of flows, and clarifies properties of porous flow fluids. It shows that, deviating from Darcy＇s linear law, the porous flow characteristics obey a nonlinear law in a low-permeability porous medium, and the viscosity of the porous flow fluid and the permeability values of water and oil are not constants. Based on these characters, a new porous flow model, which can better describe low permeability reservoir~ is established. This model can describe various patterns of porous flow, as Darcy＇s linear law does. All the parameters involved in the model, having definite physical meanings, can be obtained directly from the experiments.

A new cross-scaling method to deal with the porous flow problem

The finite volume method （FVM） and the lattice Boltzmann method （LBM） are coupled with each other to construct a new cross-scaling method to deal with the porous flow problem. To check the effectiveness of our developed cross-scaling LBM-FVM, the above mentioned problem is also solved by the well known LBM-LBM. Based on the data checking of the published data and the results of LBM-FVM and LBM-LBM, good agreement is observed.

LOCAL DISCONTINUOUS GALERKIN METHOD FOR RADIAL POROUS FLOW WITH DISPERSION AND ADSORPTION

Based on the local discontinuous Galerkin methods for time-dependent convection-diffusion systems newly developed by Corkburn and Shu,according to the form of the generalized convection-diffusion equations which model the radial porous flow with dispersion and adsorption,a local discontinuous Galerkin method for radial porous flow with dispersion and adsorption was developed,a high order accurary new scheme for radial porous flow is obtained.The presented method was applied to the numerical tests of two cases of radial porous,i.e., the convection-dispersion flow and the convection-dispersion-adsorption flow,the corresponding parts of the numerical results are in good agreement with the published solutions,so the presented method is reliable.Reckoning of the computational cost also shows that the method is practicable.

Prediction of Porous Media Fluid Flow with Spatial Heterogeneity Using Criss-Cross Physics-Informed Convolutional Neural Networks

Recent advances in deep neural networks have shed new light on physics,engineering,and scientific computing.Reconciling the data-centered viewpoint with physical simulation is one of the research hotspots.The physicsinformedneural network(PINN)is currently the most general framework,which is more popular due to theconvenience of constructing NNs and excellent generalization ability.The automatic differentiation(AD)-basedPINN model is suitable for the homogeneous scientific problem;however,it is unclear how AD can enforce fluxcontinuity across boundaries between cells of different properties where spatial heterogeneity is represented bygrid cells with different physical properties.In this work,we propose a criss-cross physics-informed convolutionalneural network(CC-PINN)learning architecture,aiming to learn the solution of parametric PDEs with spatialheterogeneity of physical properties.To achieve the seamless enforcement of flux continuity and integration ofphysicalmeaning into CNN,a predefined 2D convolutional layer is proposed to accurately express transmissibilitybetween adjacent cells.The efficacy of the proposedmethodwas evaluated through predictions of several petroleumreservoir problems with spatial heterogeneity and compared against state-of-the-art(PINN)through numericalanalysis as a benchmark,which demonstrated the superiority of the proposed method over the PINN.

Review on the Development of Oil and Gas Flow in Underground Porous Media

Through reviewing the flow theory’s birth and development history in underground porous media and contrasting the mechanics of underground fluids and mechanics of viscous fluids, this paper points out the main factors, which affect the development of the theory on oil and gas porous flow. The development law and development route of the mechanics of fluids in porous media are also summarized in this paper.

THE TRANSIENT TWO-DIMENSIONAL FLOW THROUGH DOUBLE POROUS MEDIA

This paper presents the analytical solutions in Laplace domain for two-dimensional nonsteady flow of slightly compressible liquid in porous media with double porosity by using the methods of integral transforms and variables separation. The effects of the ratio of storativities to , interporosity flow parameter on the pressure behaviors for a vertically fractured well with infinite conductivity are investigated by using the method of numerical inversion. The new log-log diagnosis graph of the pressures is given and analysed.

Evaluation of gas wettability and its effects on fluid distribution and fluid flow in porous media

The special gas wettability phenomenon of reservoir rocks has been recognized by more and more researchers.It has a significant effect on efficient development of unconventional reservoirs.First,based on the preferentially gas-covered ability and surface free energy changes,definition and evaluation methods have been established.Second,a method for altering rock wettability and its mechanisms have been studied,surface oriented phenomena of functional groups with low surface energy are the fundamental reason for gas wettability alteration of rock.Third,the effect of gas wettability on the surface energy,electrical properties and dilatability are investigated.Last,the effects of gas wettability on capillary pressure,oil/gas/water distribution and flow are investigated with capillary tubes and etchedglass network models.The gas wettability theory of reservoir rocks has been initially established,which provides theoretical support for the efficient production of unconventional reservoirs and has great significance.

Analytical solution of a double moving boundary problem for nonlinear flows in one-dimensional semi-infinite long porous media with low permeability

Based on Huang＇s accurate tri-sectional nonlin- ear kinematic equation （1997）, a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeability is presented for the case of a constant flow rate on the inner boundary. This model contains double moving boundaries, including an internal moving boundary and an external mov- ing boundary, which are different from the classical Stefan problem in heat conduction： The velocity of the external moving boundary is proportional to the second derivative of the unknown pressure function with respect to the distance parameter on this boundary. Through a similarity transfor- mation, the nonlinear partial differential equation （PDE） sys- tem is transformed into a linear PDE system. Then an ana- lytical solution is obtained for the dimensionless simplified mathematical model. This solution can be used for strictly checking the validity of numerical methods in solving such nonlinear mathematical models for flows in low-permeable porous media for petroleum engineering applications. Finally, through plotted comparison curves from the exact an- alytical solution, the sensitive effects of three characteristic parameters are discussed. It is concluded that with a decrease in the dimensionless critical pressure gradient, the sensi- tive effects of the dimensionless variable on the dimension- less pressure distribution and dimensionless pressure gradi- ent distribution become more serious; with an increase in the dimensionless pseudo threshold pressure gradient, the sensi- tive effects of the dimensionless variable become more serious; the dimensionless threshold pressure gradient （TPG） has a great effect on the external moving boundary but has little effect on the internal moving boundary.

Slip effects on shearing flows in a porous medium

This paper deals with the magnetohydrodynamic （MHD） flow of an Oldroyd 8-constant fluid in a porous medium when no-slip condition is no longer valid. Modified Darcy＇s law is used in the flow modelling. The non-linear differential equation with non-linear boundary conditions is solved numerically using finite difference scheme in combination with an iterative technique. Numerical results are obtained for the Couette, Poiseuille and generalized Couette flows. The effects of slip parameters on the velocity profile are discussed.

Theoretical investigation of micropolar fluid flow between two porous disks

The steady, laminar, incompressible and two dimensional micropolar flow between two porous disks was investigated using optimal homotopy asymptotic method(OHAM) and fourth order Runge–Kutta numerical method. Comparison between OHAM and numerical method shows that OHAM is an exact and high efficient method for solving these kinds of problems. The results are presented to study the velocity and rotation profiles for different physical parameters such as Reynolds number, vortex viscosity parameter, spin gradient viscosity and microinertia density parameter. As an important outcome, the magnitude of the microrotation increases with an increase in the values of injection velocity while it decreases by increasing the values of suction velocity.

Homotopy analysis solutions for the asymmetric laminar flow in a porous channel with expanding or contracting walls

In this paper, the asymmetric laminar flow in a porous channel with expanding or contracting walls is investigated. The governing equations are reduced to ordinary ones by using suitable similar transformations. Homotopy analysis method （HAM） is employed to obtain the expres- sions for velocity fields. Graphs are sketched for values of parameters and associated dynamic characteristics, especially the expansion ratio, are analyzed in detail.

Numerical investigations of asymmetric flow of a micropolar fluid between two porous disks

Numerical solution is presented for the two- dimensional flow of a micropolar fluid between two porous coaxial disks of different permeability for a range of Reynolds number Re （-300≤ Re 〈 0） and permeability parameter A （1.0≤A ≤2.0）. The main flow is superimposed by the injection at the surfaces of the two disks. Von Karman＇s similarity transformations are used to reduce the governing equations of motion to a set of non-linear coupled ordinary differential equations （ODEs） in dimensionless form. An algorithm based on the finite difference method is employed to solve these ODEs and Richardson＇s extrapolation is used to obtain higher order accuracy. The results indicate that the parameters Re and A have a strong influence on the velocity and microrotation profiles, shear stresses at the disks and the position of the viscous/shear layer. The micropolar material constants cl, c2, c3 have profound effect on microrotation as compared to their effect on streamwise and axial velocity profiles. The results of micropolar fluids are compared with the results for Newtonian fluids.

Volumetric lattice Boltzmann method for pore-scale mass diffusionadvection process in geopolymer porous structures

Porous materials present significant advantages for absorbing radioactive isotopes in nuclear waste streams.To improve absorption efficiency in nuclear waste treatment,a thorough understanding of the diffusion-advection process within porous structures is essential for material design.In this study,we present advancements in the volumetric lattice Boltzmann method(VLBM)for modeling and simulating pore-scale diffusion-advection of radioactive isotopes within geopolymer porous structures.These structures are created using the phase field method(PFM)to precisely control pore architectures.In our VLBM approach,we introduce a concentration field of an isotope seamlessly coupled with the velocity field and solve it by the time evolution of its particle population function.To address the computational intensity inherent in the coupled lattice Boltzmann equations for velocity and concentration fields,we implement graphics processing unit(GPU)parallelization.Validation of the developed model involves examining the flow and diffusion fields in porous structures.Remarkably,good agreement is observed for both the velocity field from VLBM and multiphysics object-oriented simulation environment(MOOSE),and the concentration field from VLBM and the finite difference method(FDM).Furthermore,we investigate the effects of background flow,species diffusivity,and porosity on the diffusion-advection behavior by varying the background flow velocity,diffusion coefficient,and pore volume fraction,respectively.Notably,all three parameters exert an influence on the diffusion-advection process.Increased background flow and diffusivity markedly accelerate the process due to increased advection intensity and enhanced diffusion capability,respectively.Conversely,increasing the porosity has a less significant effect,causing a slight slowdown of the diffusion-advection process due to the expanded pore volume.This comprehensive parametric study provides valuable insights into the kinetics of isotope uptake in porous structures,facilitating the development of porous materials for nuclear waste treatment applications.

A numerical study on heat transfer enhancement and design of a heat exchanger with porous media in continuous hydrothermal flow synthesis system

The aim of this study is to use a new configuration of porous media in a heat exchanger in continuous hydrothermal flow synthesis(CHFS)system to enhance the heat transfer and minimize the required length of the heat exchanger.For this purpose,numerous numerical simulations are performed to investigate performance of the system with porous media.First,the numerical simulation for the heat exchanger in CHFS system is validated by experimental data.Then,porous media is added to the system and six different thicknesses for the porous media are examined to obtain the optimum thickness,based on the minimum required length of the heat exchanger.Finally,by changing the flow rate and inlet temperature of the product as well as the cooling water flow rate,the minimum required length of the heat exchanger with porous media for various inlet conditions is assessed.The investigations indicate that using porous media with the proper thickness in the heat exchanger increases the cooling rate of the product by almost 40% and reduces the required length of the heat exchanger by approximately 35%.The results also illustrate that the most proper thickness of the porous media is approximately equal to 90% of the product tube's thickness.Results of this study lead to design a porous heat exchanger in CHFS system for various inlet conditions.

Simulation of flow through porous anode in MFC at higher power density

Microbial fuel cell （MFC） is a novel environmental friendly energy device which has received great attention due to its technology for producing electricity directly fi-om organic or inorganic matter by using bacteria as catalyst. To date, many experiments have been carried out to achieve the maximum power output with advective flow through porous anode to the cathode in the MFC. However, the precise mechanical mechanism of flow through anode and the quantified relationship between electrode spacing and MFC performance are not yet clearly understood. It hasbeen found experimentally that the power output can be increased apparently at certain electrode spacing configuration. Based on these available experimental data, this paper investigates the effect of spacing between electrodes, the Darcy number of porous anode and the Reynolds number on the power production performance of MFC by using lattice Boltzmann method. The numerical simulation results present that the distance between electrodes significantly influences the flow velocity and residence time of the organic matter attached to the anode in the MFC. Moreover, it is found that the Darey number of porous anode and the Reynolds number can regulate the output efficiency of MFC. These results perform better understanding of the complex phenomena of MFC and will be helpful to optimize MFC design.

Effects of Solid Matrix and Porosity of Porous Medium on Heat Transfer of Marangoni Boundary Layer Flow Saturated with Power-Law Nanofluids

The effect of the solid matrix and porosity of the porous medium are first introduced to the study of power-law nanofluids, and the Marangoni boundary layer flow with heat generation is investigated. Two cases of solid matrix of porous medium including glass balls and aluminum foam are considered. The governing partial differential equations are simplified by dimensionless variables and similarity transformations, and are solved numerically by using a shooting method with the fourth-fifth-order Runge-Kutta integration technique. It is indicated that the increase of the porosity leads to the enhancement of heat transfer in the surface of the Marangoni boundary layer flow.

■ FLOW WITH PHYSICO-CHEMICAL PROCESSES—MICROSCOPIC STUDY

This paper describes the results of microscopic study on fluid flows through porous media.The oil-water two-phase flow,the oil-air-water tri-phase flow.the Foam-surfactant-oil-water-air multi-phase flow,the microemulsion-oil-water multi-phase flow and flow with neutralization reaction are introduced.The micromodels,the technology of fabricating micromodels and the method of their application are also described.

Interstitial fluid flow:simulation of mechanical environment of cells in the interosseous membrane

In vitro experiments have shown that subtle fluid flow environment plays a significant role in living biological tissues, while there is no in vivo practical dynamical measurement of the interstitial fluid flow velocity. On the basis of a new finding that capillaries and collagen fibrils in the interosseous membrane form a parallel array, we set up a porous media model simulating the flow field with FLUENT software, studied the shear stress on interstitial cells＇ surface due to the interstitial fluid flow, and analyzed the effect of flow on protein space distribution around the ceils. The numerical simulation results show that the parallel nature of capillaries could lead to directional interstitial fluid flow in the direction of capillaries. Interstitial fluid flow would induce shear stress on the membrane of interstitial cells, up to 30 Pa or so, which reaches or exceeds the threshold values of cells＇ biological response observed in vitro. Interstitial fluid flow would induce nonuniform spacial distribution of secretion protein of mast cells. Shear tress on cells could be affected by capillary parameters such as the distance between the adjacent capillaries, blood pressure and the permeability coefficient of capillary＇s wall. The interstitial pressure and the interstitial porosity could also affect the shear stress on cells. In conclusion, numerical simulation provides an effective way for in vivo dynamic interstitial velocity research, helps to set up the vivid subtle interstitial flow environment of cells, and is beneficial to understanding the physiological functions of interstitial fluid flow.

SENSITIVITY COEFFICIENTS OF SINGLE-PHASE FLOW IN LOW-PERMEABILITY HETEROGENEOUS RESERVOIRS

Theoretical equations for computing sensitivity coefficients of wellbore pressures to estimate the reservoir parameters in low-permeability reservoirs conditioning to non-Darcy flow data at low velocity were obtained. It is shown by a lot of numerical calculations that the wellbore pressures are much more sensitive to permeability very near the well than to permeability a few gridblocks away from the well. When an initial pressure gradient existent sensitivity coefficients in the region are closer to the active well than to the observation well. Sensitivity coefficients of observation well at the line between the active well and the observation well are influenced greatly by the initial pressure gradient.

Development of a new correlation to calculate permeability for flows with high Knudsen number

Flows with high Knudsen number play a prominent role in many engineering applications. The present study is an effort toward the simulation of flow with high Knudsen number using modified lattice Boltzmann method （LBM） through a porous medium in a channel. The effect of collision between molecules and solid walls, which is required to accurately simulate transition flow regime, is taken into account using a modified relaxation time. Slip velocity on the wall, which is another significant difficulty in simulating transition flow regime, is captured using the slip reflection boundary condition （SRBC）. The geometry of porous medium is considered as in-line and staggered. The results are in good agreement with previous works. A new correlation is obtained between permeability, Knudsen number and porosity for flows in transition flow regimes.